206 



PIERCE. 



Let us now decompose the coefficient of the first integral of (31) as 

 follows : 



1 , cos- G 1 , , ,, cos^ G 



1 1 + cos 2 G 



4 4 



cos2G 



+ cos2 G 



+ cos2 G. 



Then the whole equation (31) may be written 



2/2 



p = — cos 

 c 



^^f (rf-ro)|^ 



sin^ B sin^ £ sin 2 ^ 



2 



cos 2 6! p^a 

 4 Jo 



— cos 7) dy sin 



2G 



1 



4A 



sm7 

 7 4 Jo 7 



, 2 /^ r^'^ (1 — cos 7) c?7 sin 2 G T^'* sin 7 

 Jo 7 2 Jo 7 



(Z7 

 c?7 



(34) 



The various integrals may now be obtained by expanding in series 

 and integrating term by term. This gives 



P = 



2P 



cos'' 



|(ct-ro)[ 



sin ^B f sin 2 A 



2 V 2A 



cos 2G 



(44)2 

 2!2 



(4Ay (44 )« 



+ 



1 + cos 2G { {2A) 



2!2 



4!4 



(MY 



4!4 



+ 



+ 



sm 



2Gj 

 4 I 

 sin 2(? 



2A -(MZ + 

 ^"^ 3!3 + 



6!6 



(2/i)« 

 6!6 



(MZ 



5!5 



(2Af 

 5!5 



(35) 



Let us now eliminate B from the first terms of this equation, by 

 substituting B = G — A, obtaining 



